Comptes Rendus
Divergence-free condition in transport simulation
Comptes Rendus. Mécanique, Volume 344 (2016) no. 9, pp. 642-648.

In this work, two adaptations of the particle method allowing one to reduce the numerical errors induced by the non-zero divergence of flow fields in the numerical simulations of particle transport are presented. The first adaptation is based on the renormalization method allowing one to use an irregular distribution of particles induced by the non-zero divergence of flow fields. The second adaptation consists in applying a correction on the weight of the particles by using the relation between the divergence of flow fields and the particles' volume evolution. This adaptation may be considered as a relaxation method. The accuracy of both methods is evaluated by simulating the transport of an inert tracer by the flow of a jet in crossflow whose concentration fields were measured experimentally. The comparison between the numerical and experimental results shows clearly that the two adaptations of the particle method correct efficiently the effect of a non-zero divergence velocity field on the computed concentration.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2016.02.007
Keywords: Divergence-free condition, Particle method, Renormalization method, Relaxation method

Adrien Berchet 1; Anthony Beaudoin 1; Serge Huberson 1

1 Institute of Pprime, SP2MI-Téléport 2, boulevard Marie-et-Pierre-Curie, BP 30179, 86962 Futuroscope Chasseneuil-du-Poitou cedex, France
@article{CRMECA_2016__344_9_642_0,
     author = {Adrien Berchet and Anthony Beaudoin and Serge Huberson},
     title = {Divergence-free condition in transport simulation},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {642--648},
     publisher = {Elsevier},
     volume = {344},
     number = {9},
     year = {2016},
     doi = {10.1016/j.crme.2016.02.007},
     language = {en},
}
TY  - JOUR
AU  - Adrien Berchet
AU  - Anthony Beaudoin
AU  - Serge Huberson
TI  - Divergence-free condition in transport simulation
JO  - Comptes Rendus. Mécanique
PY  - 2016
SP  - 642
EP  - 648
VL  - 344
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crme.2016.02.007
LA  - en
ID  - CRMECA_2016__344_9_642_0
ER  - 
%0 Journal Article
%A Adrien Berchet
%A Anthony Beaudoin
%A Serge Huberson
%T Divergence-free condition in transport simulation
%J Comptes Rendus. Mécanique
%D 2016
%P 642-648
%V 344
%N 9
%I Elsevier
%R 10.1016/j.crme.2016.02.007
%G en
%F CRMECA_2016__344_9_642_0
Adrien Berchet; Anthony Beaudoin; Serge Huberson. Divergence-free condition in transport simulation. Comptes Rendus. Mécanique, Volume 344 (2016) no. 9, pp. 642-648. doi : 10.1016/j.crme.2016.02.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.02.007/

[1] T. Kitada Effect of non-zero divergence wind fields on atmospheric transport calculations, Atmos. Environ., Volume 21 (1987) no. 4, pp. 785-788

[2] M.A. Nunez; R. Mendoza Structural instability of atmospheric flows under perturbations of the mass balance and effect in transport calculations, in: VIIth International Congress of Engineering Physics, J. Phys. Conf. Ser., Volume 582 (2015)

[3] C.R. Anderson; C. Greengard Vortex Dynamics and Vortex Methods, American Mathematical Society, 1991

[4] G.H. Cottet; P.D. Koumoutsakos Vortex Methods: Theory and Practice, Cambridge University Press, 2000

[5] R.A. Gingold; J.J. Monaghan Smoothed particle hydrodynamics—theory and application to non-spherical stars, Mon. Not. R. Astron. Soc., Volume 181 (1977), pp. 375-389

[6] Z. Chena; Z. Zongb; M.B. Liud; L. Zoub; H.T. Lib; C. Shua An SPH model for multiphase flows with complex interfaces and large density differences, J. Comput. Phys., Volume 283 (2015), pp. 169-188

[7] J.T. Beale On the accuracy of vortex methods at large times, Computational Fluid Dynamics and Reacting Gas Flows, The IMA Volumes in Mathematics and Its Applications, vol. 12, 1988, pp. 19-32

[8] P. Ploumhans; G.S. Winckelmans; J.K. Salmon; A. Leonard; M.S. Warren Vortex methods for direct numerical simulation of three dimensional bluff body flows: application to the sphere at Re=300, 500 and 1000, J. Comput. Phys., Volume 178 (2002), pp. 427-463

[9] A. Berchet; L. Thomas; P. Braud; L. David Instantaneous volumic concentration and velocity measurements of a jet in crossflow for the evaluation of the entrainment, Exp. Fluids, Volume 54 (2013) no. 12, p. 1608

[10] R. Vernet; L. Thomas; L. David Analysis and reconstruction of a pulsed jet in crossflow by multi-plane snapshot POD, Exp. Fluids, Volume 47 (2009), pp. 707-720

[11] A. Jolles; S. Huberson Correction of the projection error in particle mesh methods, Rech. Aérosp., Volume 4 (1990), pp. 1-6

Cited by Sources:

Comments - Policy